Some GKZ-hypergeometric systems of Feynman integrals with codimension\(=0\) 
or codimension\(=1\)  is presented in Ref [1]}, [2]}
through the Lee-Pomeransky parametric representations [3]}.
To construct canonical series solutions with suitable independent variables,
one should compute the restricted \(D\) -module of GKZ-hypergeometric system originating from
the Lee-Pomeransky representations on corresponding hyperplane in the parameter
space [4]}, [5]}, [6]}.
For some Feynman diagrams, the corresponding GKZ-hypergeometric systems
are obtained from the Mellin-Barnes representations [7]}, [8]}, [9]} through Miller's
transformation [10]}, [11]}.
Ref.[12]} explores the idea to bootstrap Feynman integrals using integrability,
The authors of Ref.[13]} applies the GKZ description of periods to solve the
l-loop banana amplitudes with their general mass dependence, and completely clarify
the analytic structure of all banana amplitudes with arbitrary masses [14]}.
The updated summary on some classical and modern aspects of hypergeometric
differential equations is given in literature [15]}.
A Mathematica package for integrating families of Feynman integrals
order-by order in the dimensional regulator from their GKZ-systems
is also given in literature [16]}.
A specialized integration algorithm for parametric Feynman integrals
with tame kinematics also presented in literature [17]}.
Actually Cohen-Macaulay Property of Feynman Integral indicates
that the process of finding a series representation of these
integrals is fully algorithmic [18]}, and regular
singularities of Feynman Integral are determined by its Landau Discriminant [19]}.
Furthermore, Ref. [20]} elaborates on the connection between GKZ-systems, de
Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman Integrals,
and Ref. [21]} presents a Mathematica package to find linear transformations
for some classes of multivariable hypergeometric functions. In literature [22]}
the class of \(N\)  loop massive scalar self-energy diagrams with \(N+1\)  propagators
is studied, and the new convergent series representations for the two-loop sunset diagram
with three different propagator masses and external momentum are obtained in
Ref.[23]}. The relationship between Feynman diagrams and hypergeometric functions
is reviewed in the Ref. [24]}.
